Answer
$\left(\dfrac{5\sqrt2}{2},\dfrac{5\sqrt3}{2}\right)$
Work Step by Step
The midpoint of the two points $(x_1,y_1)$ and $(x_2,y_2)$ is the point $\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$
$\left(\dfrac{2\sqrt{2}+3\sqrt2}{2},\dfrac{-2\sqrt3+7\sqrt3}{2}\right) = \left(\dfrac{5\sqrt2}{2},\dfrac{5\sqrt3}{2}\right)$